Physics 846 (Winter, 2010)

[Introduction and General Format|Syllabus]
[Problem Sets| Suggested Reading]
[Offices Hours; Grader| [Lecture Notes| Random Information]

Introduction and General Format

Physics 846 is the first quarter of a two-quarter graduate sequence on statistical physics. The text will be "Statistical Physics," 2nd edition, by R. K. Pathria (Butterworth-Heinemann, Oxford, UK and Woburn Ma, 1996); ISBN 0 7506 2469 8; list price $94.95, currently available on for $71.21 or less). A recommended text for the first part of the course is "Thermodynamics and an Introduction to Thermostatistics,'' 2nd edition, by Herbert B. Callen (John Wiley & Sons, 1985); ISBN 0-471-86256-8 (paperback); list price $110.60, currently available on for $80.99 or less).

The instructor is David Stroud. The grader is Ranjan Laha (room PRB3031, tel. 614-247-8463, email

We will meet in Smith Lab, Room 1180, on Tuesdays and Thursdays from 9:30 to 10:18 and 10:30 to 11:18.

Grades will be based on one midterm (about 25%), a final (about 40%), and homework (about 35%).

The midterm will take place on Thursday, February 11 and will last about one hour, twenty minutes. THE FINAL EXAM WILL BE GIVEN MARCH 15 FROM 9:30 TO 11:18 IN MP1046. NOTE CHANGE OF DATE FROM THAT PREVIOUSLY ANNOUNCED. ALSO NOTE THAT THE ROOM IS DIFFERENT FROM OUR USUAL ONE.

Besides the principal textbook and recommended supplementary text, I may occasionally take some material from various other books. Some other leading books on the subject of statistical physics are the following. I hope to add more to this list shortly:

``Statistical Mechanics,'' by Kerson Huang (1987). Originally written in the 1960's, very good on such topics as the Ising model and liquid helium. Quite readable.

``Thermal Physics,'' by Charles Kittel and Herbert Kroemer (1980). Written as an advanced undergrad textbook, but has all the basics of statistical physics and many applications in condensed matter physics.

``Statistical Physics of Particles,'' by Mehran Kardar (2007). A rather original presentation of statistical physics, with lots of applications. Last year's text.

``Statistical Physics of Fields,'' by Mehran Kardar (2007). This is a more advanced text, developed from the lectures of a leading researcher in the field. An extremely clear description of such topics as fluctuation phenomena, renormalization and scaling theory, stochastic dynamics, etc.

``A Modern Course in Statistical Physics,'' by L. E. Reichl. Includes both thermodynamics and statistical mechanics. Used as a text in this course a couple of years ago.

``Introduction to Modern Statistical Mechanics,'' by David Chandler. A text by a leading practitioner in the area of chemical physics. This book includes a compact but lucid discussion of the standard material, and also has chapters on numerical techniques such as Monte Carlo methods. See also the companion solution manual.

``Statistical Mechanics: A Set of Lectures,'' by Richard P. Feynman (paperback edition, 1998). Somewhat advanced if you haven't had much previous exposure to statistical physics, but full of original insights, new methods, and important applications.

``Statistical Mechanics, 2nd Edition'' by R. Kubo, H. Ichimaru, T. Usui, N. Hashitsume (North-Holland, 1988). Old but a clear and readable introduction, with a large number of solved examples and problems.

``Statistical Physics, Third Edition, Part 1'' by L. D. Landau and E. M. Lifshitz. A famous text, somewhat updated here.

``Statistical Physics, Part 2,'' by E. M. Lifshitz and L. P. Pitaevskii. More advanced material, such as normal Fermi liquid, Green's functions for Fermi systems, and other problems in many body physics.

``Lectures on Phase Transitions and the Renormalization Group,'' by Nigel Goldenfeld (1992). A clear and quite detailed exposition of this important topic. May be useful for part of the second quarter of this sequence.


The syllabus will be similar to that described in the course catalog, but I hope to spend no more than four weeks on thermodynamics. Topics to be covered include fundamental postulates of thermodynamics, entropy, definition of thermodynamic potentials such as internal energy, Gibbs and Helmholtz free energies, and enthalpy, changes of phase and phase transitions, microscopic expression for entropy, basis of ensemble theory including, I hope, microcanonical, canonical, and grand canonical ensembles. Most likely I will not reach quantum statistics this quarter.

Note: a good online math reference is, which has lots of analysis, plus a great deal of information about special functions. Two good books are "Tables of Integrals, Series, and Products," 6th ed., by Gradshteyn, Ryzhik, Jeffrey, and Zwillinger (Academic, San Diego, 2000), and "Mathematical Methods for Physicists," by Arfken, Weber, and Weber (Academic, San Diego, 2001).

Problem Sets

I plan to have weekly problem sets, mostly due on Thursdays. If possible, turn in the problem sets into the mailbox of the grader, Ranjan Laha, in PRB. Alternately, you may turn them into my mailbox, turn them in during class, hand them to me in my office, or or slip them under my office door (2048PRB) if I am not there.

In calculating the homework grade, I will sum up the homework scores, and convert the sum to a percent.

In general, I do not object if you discuss the problems with one another while working on them. However, you should write up your solutions independently.

oProblem Set 1.

oSolutions to PS1.

oProblem Set 2.

oSolutions to PS2.

oProblem Set 3.

oSolutions to PS3

oProblem Set 4.

oSolutions to PS4

oProblem Set 5.

oSolutions to PS5.

oProblem Set 6.

oSolutions to PS6.

oProblem Set 7.

oSolutions to PS7.

Office Hours; Grader

My office is Room 2048 of the Physics Research Building. My office telephone no. is 292-8140 and my email address is My office hours will be Tu 11:30 - 12:30 and Th 1 - 2. You can also see me by appointment, or you can simply drop by, and I am generally happy to talk to you if I do not have another visitor. Please consult the grader, Ranjan Laha, if you have any questions about the homework grading.

Lecture Notes

I expect to post my (hand-written) lecture notes as I complete them. They are posted as a study aid but they are not guaranteed to be error-free.

oLecture of January 5 (thermodynamic equilibrium; work, heat, and internal energy; fundamental relation; entropy maximum postulates)

o Lecture of January 7 (equilibrium with respect to heat flow, volume change, and matter flow: temperature, pressure, and chemical potentials; chemical equilibrium; Euler relation; Gibbs-Duhem relation; equations of state of a monocomponent ideal gas)

oLecture of January 12 (examples of equations of state: ideal gas, electromagnetic radiation, multicomponent ideal gas, van der Waals fluid; entropy of mixing; various thermodynamic derivatives)

oBrief supplementary notes on one-component and multicomponent ideal gas.

oLecture of January 14 (processes, engines, maximum work theorem, quasistatic processes, reversible processes; examples; definitions of engine efficiency, coefficients of refrigerator and heat pump performance).

oLecture of January 19 (Carnot cycle, measurability of temperature and of entropy, other cyclic processes, energy-minimum principle, definitions of Helmholtz and Gibbs free energy and of enthalpy, some examples of Legendre transformations).

oLecture of January 21 (minimum principles for various free energies, Joule-Thomson process, chemical reactions and heat of reaction, identities related to partial derivatives, brief treatment of Jacobians, Maxwell relations, applications).

oLecture of January 26 (thermodynamic stability conditions; stable and unstable free energy isotherms; phase diagram of a one-component material in the P-T plane; first-order phase transitions).

oLecture of January 28 (phase diagrams of a one-component system; triple point and critical point; Clausius-Clapeyron equation; unstable isotherms; critical point of the van der Waals gas).

oLecture of February 2 (start of statistical mechanics: entropy as the log of the number of microstates; application to Einstein model of harmonic oscillators; application to N two-level systems; approximation for log(N!) for large N. Note: not all of this was covered on Feb. 2. )

oLectures of February 4 and 9 (Hamilton's equations, concept of phase space, concept of an ensemble of systems and an ensemble average; Liouville's theorem)

oLecture of Feb. 18 (classical microcanonical ensemble).

oLecture of Feb. 23 (classical canonical ensemble).

oLecture of Feb. 25 (equipartition theorem, applications, classical and quantum harmonic oscillator in the canonical ensemble, Maxwell-Boltzmann velocity distribution, virial theorem. Note: there is more material in the posted notes than I covered in class.)

oLecture of March 2 (more applications of canonical ensemble: more on quantum harmonic oscillator; two-level systems; spins in a magnetic field.)

oLecture of March 4 (start of grand canonical ensemble. I did not get through all this material on Thursday and will complete discussion next Tuesday.)

oLecture of March 9 (more on grand canonical ensemble, including severa examples).

Random Information

oJ. Willard Gibbs

o Nicolas Leonard Sadi Carnot

o Rudolf Julius Emmanuel Clausius

oJames Clerk Maxwell

oLudwig Boltzmann

oWalther Nernst

oSatyendra Nath Bose

oAlbert Einstein

o Max Planck

oEnrico Fermi

oPaul Adrien Marie Dirac

oKenneth G. Wilson